Question

Work out the area of this circle.

Take to be 3.142 and write down all the digits given by your calculator.
10 cm

please help !!

Answer 1

Area is 314.2 cm²

Explanation:

- Consider a circle whose radius is r, while calculating its area, the formula is derived from its circumference;

`{ \rm{circumference = 2\pi r}}`

- but area is the integral of circumference;

`{ \rm{area = \int circumference }} \\ \\ { \rm{area = \int2\pi r \: dr}}`

- Assume area is between the center to the edge from r = 0 to r = r

`{ \rm{area = 2\int^(r)_(0)\pi r \: dr}} \\ \\ { \rm{area = 2[\pi ( \frac{ {r}^(2) }{2} )]^(r) _(0) }} \\ \\ { \rm{area = \pi {(r)}^(2) - \pi {(0)}^(2) }} \\ \\ { \boxed{ \rm{area = \pi {r}^(2) }}}`

- From the question given, the circle has a radius of 10cm

`{ \rm{area = 3.142 * {10}^(2) }} \\ \\ { \bf{area = 314.2 \: {cm}^(2) }}`

`{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}`